Page History

{latex}
\large
$$
\left( {\Delta h_{FCMFC} A_{float} \rho g} \right)L_{float\;lever\;arm}  = \left( {\rho g\Delta h_{stock} A_{orifice} } \right)L_{valve\;lever\;arm}
$$
{latex}
where {latex}$\Delta h_{FCM}${latex} is the change in depth of the liquid level in the constant head tank and {latex}$A_{float}${latex} is the cross sectional area of the cylindrical float. Thus {latex}$\Delta h_{FCM} A_{float}${latex} is the submerged volume of the float that when multiplied by the density, {latex}$\rho${latex} and by acceleration due to gravity is equal to the total buoyant force acting on the float. The lever arm for the float has a length {latex}$L_{float\;lever\;arm}${latex}. The moment acting to open the valve is provided by the pressure of liquid from the stock tank, {latex}$\rho g\Delta h_{stock}${latex}, acting over the area of the valve opening {latex}$A_{orifice}${latex}. The lever arm for the opening moment is  {latex}$A_{orifice}${latex}

{latex}
The derivative of the function $f(x)$ at the point $x_0$ is
\begin{equation}
f'(x_0) =
\lim_{x \rightarrow x_0}
\frac{f(x) - f(x_0)}{x - x_0}
\end{equation}
{latex}